A so-called umbrella 1 with two layers of umbrella cover as indicated in FIG. 1 mainly is combined with an independent upper layer umbrella cover 2 and a lower layer umbrella cover 3 to discharge the strong wind from their clearance and disperse the wind pressure to prevent the possible damage to ribs of said umbrella. The rib structure of a known umbrella 1 with two layers of umbrella cover (as described in U.S. Pat. No. 6,681,784) is set with a wind resisting rib 600 that is combined of a thinner metal bar with a ball tail 601 in one and with another end bent downwards to form the first circular ring 602 then extended a shorter bar toward the ball tail 601 and formed the second circular ring 603. As indicated in FIG. 2, a front edge of the upper umbrella cover 10 is mounted on the rib connecting nest 700 of the umbrella. A rear edge is mounted on the ball tail 601 of the wind resisting rib 600 by a silk wire, and is mounted with the first circular ring 602 by a silk wire as well. Furthermore, a front edge of the lower umbrella cover 20 is mounted on the second ring 603 by a silk wire, and a rear edge is mounted on the ball tail of the last folded rib 300 to form an umbrella with two layers of umbrella cover. However, this kind of structure can obviously be realized that said wind resisting rib 600 has no connection with the ribs of the umbrella. Therefore the umbrella with two layers of umbrella cover will lose its winding resisting effects due to the random swing of the wind resisting rib along with the upper, lower umbrella cover 10, 20. As further indicated in FIG. 3, the said structure is mounted a first circular ring 602 in the wind resisting rib 600 on the rivet 312 of an assembling seat 310 of a last folded rib 300 of the umbrella rib. Although this kind of set up can position the wind resisting rib 600, it will also cause the problems of cost increase owing to the necessity of removing the rivets.